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Security Chapters 14,15

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The Security Environment Threats Security goals and threats

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Basics of Cryptography Relationship between the plaintext and the ciphertext

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Monoalphabetic substitution –each letter replaced by different letter Given the encryption key, –easy to find decryption key Secret-key crypto called symmetric-key crypto Secret-Key Cryptography

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Public-Key Cryptography All users pick a public key/private key pair –publish the public key –private key not published Public key is the encryption key –private key is the decryption key

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RSA Encryption To find a key pair e, d: 1. Choose two large prime numbers, P and Q (each greater than 10100), and form: N = P x Q Z = (P–1) x (Q–1) 2. For d choose any number that is relatively prime with Z (that is, such that d has no common factors with Z). We illustrate the computations involved using small integer values for P and Q: P = 13, Q = 17 –> N = 221, Z = 192 d = 5 3.To find e solve the equation: e x d = 1 mod Z That is, e x d is the smallest element divisible by d in the series Z+1, 2Z+1, 3Z+1,.... e x d = 1 mod 192 = 1, 193, 385,... 385 is divisible by d e = 385/5 = 77

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RSA Encryption (contd.) To encrypt text using the RSA method, the plaintext is divided into equal blocks of length k bits where 2 k < N (that is, such that the numerical value of a block is always less than N; in practical applications, k is usually in the range 512 to 1024). k = 7, since 2 7 = 128 The function for encrypting a single block of plaintext M is: (N = P X Q = 13X17 = 221), e = 77, d = 5: E'(e,N,M) = M e mod N for a message M, the ciphertext is M 77 mod 221 The function for decrypting a block of encrypted text c to produce the original plaintext block is: D'(d,N,c) = c d mod N The two parameters e,N can be regarded as a key for the encryption function, and similarly d,N represent a key for the decryption function. So we can write K e = and K d =, and we get the encryption function: E(K e, M) ={M} K (the notation here indicating that the encrypted message can be decrypted only by the holder of the private key K d ) and D(K d, ={M} K ) = M. - public key, d – private key for a station

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Application of RSA Lets say a person in Atlanta wants to send a message M to a person in Buffalo: Atlanta encrypts message using Buffalo’s public key B E(M,B) Only Buffalo can read it using it private key b: E(b, E(M,B)) M In other words for any public/private key pair determined as previously shown, the encrypting function holds two properties: –E(p, E(M,P)) M –E(P, E(M,p)) M

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How can you authenticate “sender”? In real life you will use signatures: we will look at concept of digital signatures next. Instead of sending just a simple message, Atlanta will send a signed message signed by Atlanta’s private key: –E(B,E(M,a)) Buffalo will first decrypt using its private key and use Atlanta’s public key to decrypt the signed message: –E(b, E(B,E(M,a)) E(M,a) –E(A,E(M,a)) M

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Digital Signatures Strong digital signatures are essential requirements of a secure system. These are needed to verify that a document is: Authentic : source Not forged : not fake Non-repudiable : The signer cannot credibly deny that the document was signed by them.

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Digest Functions Are functions generated to serve a signatures. Also called secure hash functions. It is message dependent. Only the Digest is encrypted using the private key.

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Alice’s bank account certificate 1.Certificate type:Account number 2.Name:Alice 3.Account:6262626 4.Certifying authority:Bob’s Bank 5.Signature:{Digest(field 2 + field 3) } K bpr iv

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Digital signatures with public keys

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Low-cost signatures with a shared secret key

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One-Way Functions Function such that given formula for f(x) –easy to evaluate y = f(x) But given y –computationally infeasible to find x

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Digital Signatures Computing a signature block What the receiver gets (b)

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Protection Mechanisms Protection Domains (1) Examples of three protection domains

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Protection Domains (2) A protection matrix

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Protection Domains (3) A protection matrix with domains as objects

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Access Control Lists (1) Use of access control lists of manage file access

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Access Control Lists (2) Two access control lists

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Capabilities (1) Each process has a capability list

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Cryptographically-protected capability Generic Rights 1.Copy capability 2.Copy object 3.Remove capability 4.Destroy object Capabilities (2) ServerObjectRightsf(Objects, Rights, Check)

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Summary We studied fundamental concepts in security and protection. If you are interested in this topic you can pursue a graduate degree on this topic.

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